chapter 13: introduction to enzymes

Lecture 7 Slide 1Biochemistry 2000

Chapter 13:Chapter 13:Introduction to EnzymesIntroduction to Enzymes

Voet & Voet: Voet & Voet: Pages 469-481Pages 469-481


IntroductionIntroduction

Virtually all biochemical reactions in an organism are mediated by remarkable biological catalysts – enzymes

Enzymes are a category of protein that differ from ordinary chemical catalysts in several respects

(1) Higher reaction rates

● several orders faster than equivalent chemical catalysts

● 106-1012 rate enhancement

(2) Milder reaction conditions

● low temperature, atmospheric pressure, narrow pH range, etc.

(3) Greater reaction specificity

● Narrow range of substrate and product specificities

● stereospecificity, lack of side products

(4) Capacity for regulation

● “fine” control of reaction rate


Substrate BindingSubstrate Binding

Substrate binding to a protein is governed by the same noncovalent forces that apply to protein structure

Binding sites are:

1) generally an indentation or cleft on the surface of the enzyme molecule

2) complementary in shape (includes chirality) to the substrate (geometric complementarity)

3) complementary in electrostatic surface potentials to the substrate (electronic complementarity)

● charge or partial charge associated with each point along the surface of a protein

Only complementary (geometric and electronic) substrates bind to an enzyme binding site (via noncovalent forces)


Enzyme Binding SitesEnzyme Binding Sites(substrate binding)(substrate binding)

Two major hypothesis

(1) Lock-and-key

– Enzyme active site is preformed in the absence of substrate

– Enzyme is the lock and the substrate is the key

(2) Induced fit

– Enzyme active site only forms in the presence of substrate

– Substrate provides stabilizing energetic interactions that are otherwise unavailable

Structural data suggest enzyme active sites are largely preformed with most demonstrating at least some induced fit


SpecificitySpecificity

Enzyme specificity – the range of compounds that can be used as substrates

Specificity of enzymes vary widely

– a few enzymes are specific for a single compound

– most enzymes catalyze the reactions of a small range of related compounds

● eg. YADH can utilize methanol (40%) and propanol (4%) at reduced efficiency compared to the natural substrate (ethanol; 100%)

– some enzymes (eg. digestive enzymes) are so 'promiscuous' it is more appropriate to talk of preference than specificity

● eg. cleave all peptide bonds except before proline

Enzymes are strictly stereospecific

eg. Proteases only hydrolyze polypeptides composed of L-amino acids, Glycolysis is specific for D-glucose, ...

High specificity

Low specificity


Cofactors Cofactors

Protein functional groups are not suited to all types of reactions

● proteins have evolved binding sites for (small molecule) cofactors that participate in catalysis

● range in size from ions (eg. Zn2+, Ca2+) to large organic molecules known as coenzymes (transiently associate) and prosthetics (permanent association)

Nomenclature for enzymes that bind cofactors

Holoenzyme: enzyme plus cofactor (active)

Apoenzyme: enzyme without cofactor (inactive) Many vitamins are organic cofactors


Regulation of Enzyme ActivityRegulation of Enzyme Activity

Cells must regulate catalytic activity of enzymes in order to coordinate its metabolic processes

Two general approaches

(1) Cells can regulate catalytic activity by varying the amount of enzyme

● synthesis of new enzyme or degradation of existing enzyme (eg. constant activity, variable amount)

(2) The activity of an enzyme may be regulated directly

● subtle conformational changes increase or decrease affinity for substrate and alter catalytic activity

● structural alterations result from either:

a) non-covalent binding of regulatory molecule (eg. steric inhibition, effector binding)

b) covalent modification of enzyme (eg. zymogen activation, modification)


Allostery & CooperativityAllostery & Cooperativity

Regulation of enzyme activity through conformational change

(1) allostery – binding at effector site alters binding affinity for different ligand at the functional site (eg. catalytic)

● eg. ATP binding to ATCase enhances binding affinity for normal substrates

(2) cooperativity – binding of a ligand at functional site (eg. binding site) alters binding affinity for same ligand at other similar functional sites.

● eg. O2 binding to Hemoglobin enhances binding affinity for O

2

In each case, the activity of enzyme is regulated by a binding induced conformational change that is transmitted throughout the quaternary structure.


NomenclatureNomenclature

Effector molecule – any molecule that regulates the binding affinity of a protein or enzyme.

Effector molecules are further subdivided based upon:

(I) activator/inhibitor

– activators increase binding affinity for substrate

– inhibitors decrease binding affinity for substrate

(II) homotropic/heterotropic

– homotropic effectors are the same as the ligand or substrate

– heterotropic effectors are different from the ligand or substrate

Cooperativity is always associated with homotropic effectors while allostery is typically associated with heterotropic effectors


Feedback inhibition of pathwayFeedback inhibition of pathway

Feedback inhibition - pathway product is heterotropic inhibitor of the enzyme catalyzing the first committed step of the pathway

Example:

ATCase catalyzes the committed step for pyrimidine biosynthesis

CTP is the product of the pyrimidine biosynthesis pathway

● CTP is also a heterotropic inhibitor (allosteric inhibitor) of ATCase


Regulation of ATCaseRegulation of ATCase

I) Feedback inhibition

(Normal case) ATCase funnels aspartate and carbamoyl phosphate from intracellular pools into pyrimidine biosynthesis (committed step)

● at sufficiently high [CTP], CTP will bind to ATCase and heterotropically inhibit the enzyme

● low [CTP] lead to dissociation of CTP and removal of heterotropic inhibition

[CTP] directly regulates CTP production via inhibition of ATCase

II) ATP activation

(Excess purine) The relative [ATP] and [CTP] represent the amounts of purine and pyrimidine nucleotides in the cell and must be regulated

● if [purine] and [pyrimidine] are out of balance, ATP binding as a heterotropic activator increases pyrimidine biosynthesis to limit excess [purine]

[ATP] regulates CTP (pyrimidine):ATP (purine) ratio via activation of ATCase


ATCase: Structure & RegulationATCase: Structure & Regulation

Regulatory chains – yellow; Catalytic chains – red & blue

R state has red and blue trimers separated (~10 Å) and rotated (12°) relative to T state

● subunit contacts are sufficiently large and tightly coupled that the T --> R transition occurs simultaneously throughout ATCase

ATP binding stabilizes the R state and CTP binding stabilizes the T state

● bind to overlapping site on edge of regulatory chain over 60 Å from active site

T state (inactive) R state (active)


Chapter 14:Chapter 14:Rates of Enyzmatic Rates of Enyzmatic

ReactionsReactions

Voet & Voet: Voet & Voet: Pages 482-506Pages 482-506


IntroductionIntroduction

Kinetics - study of the rates at which chemical reactions occurs

Major purpose is to understand reaction mechanism (the sequence of steps that result in catalysis)

Enzyme Kinetics have enormous practical importance:

(1) catalytic rate and binding affinities of substrates & inhibitors

(2) determination of catalytic mechanism

– especially powerful in combination with structural information

– involves examining catalytic rate under a variety of conditions

(3) role in metabolism

– role within pathway

(4) assays

– clinical tests and research experiments


Chemical KineticsChemical Kinetics

● Overall reaction of a reactant (A) forming a product (P) may actually involve a sequence of elementary reactions

– elementary reactions create and/or utilize reaction intermediates (I)

● Reaction mechanism involves a description of all elementary reactions in an overall reaction

● At constant T, reaction rates vary with [substrate] in a simple manner expressed as the rate equation

– k is the rate constant

– lower case letters are coefficients from a balanced chemical equation and indicate stoichiometry

– [upper case letters] are substrate concentrations

A P

A I2

I1

P

aA + bB + ... + zZ P

Rate = k [A]a [B]b ... [Z]z

Overall Reaction

(Possible) Elementary Reactions

General Single Product Reaction

Rate equation


Reaction OrderReaction Order

In the general chemical reaction for a process with a single product

● typically, the sum of (a + b + ... + z) is the reaction order

corresponds to the number of molecules that must simultaneously collide in an elementary reaction

Elementary reactions in biological systems are 1st order (unimolecular) or 2nd order (bimolecular)

– 3rd order (termolecular) elementary reactions are unusual and higher order are unknown

aA + bB + ... + zZ P

Rate = k [A]a [B]b ... [Z]z

General Single Product Reaction

Rate equation

1st order

2nd order


Reaction RatesReaction Rates

Reaction rates can be experimentally determined by following the concentrations of reactants and/or products over time

First order reaction rate equation (A --> P)

● v is the instantaneous rate or velocity of a reaction

Second order reaction rate equation (2A --> P)

Second order reaction rate equation (A + B --> P)

v=−d[A]

dt=k [A]

v=−d[A]

dt=k [A]

2

v=−d[A]

dt=−d

[B]

dt=k [A][B ]

ln [ A]=ln [Ao]−kt

1[ A]

=1

[ Ao]kt

Note: rate constant, k, has different units for 1st (s-1) and 2nd order (M-1s-1) reactions


Transition StateTransition State

Consider a bimolecular elementary reaction,

Ha – H

b + H

c --> H

a + H

b – H

c

– Hc must approach H

a-H

b sufficiently closely to

form a bond with Hb as the H

a-H

b bond breaks

The transition state is an unstable chemical structure that represents a free energy maxima on a reaction coordinate diagram

– transition state formation and breakdown are the rate determining processes for most reactions

Note: reaction coordinate is the minimum free energy pathway of a reaction


Rate determining stepRate determining step

Multistep chemical reactions are common

● Rates of the elementary reactions are often different

– if one step is significantly slowly than the others it will form a bottleneck in the overall reaction

– the slowest step in the overall reaction is referred to as the rate determining step

Reaction coordinate diagram for an overall reaction with two elementary reaction steps

– Transition state theory tells us the free energy difference between reactant and transition state reflect rate and the slowest step has the largest difference

– two cases – step 1 slow (green); step 2 slow (red)

k1=[ I ] /[ A]

k 2=[P] /[ I ]

A I P


Catalysts (Enzymes)Catalysts (Enzymes)

Catalysts enhance reaction rates by lowering the activation barrier, G‡ for the reaction they catalyze

● rate enhancement is exp(-G‡/RT), where G‡cat

is the difference in activation energy between catalyzed and uncatalyzed reactions

Thermodynamics: 10 fold rate enhancement results from a 5.7 kJ/mol decrease in G‡

cat

(106 fold enhancement requires 34.2 kJ/mol decrease)

Catalysts enhance the rates of both forward and backwards reactions equally

– Catalysts cannot change the equilibrium

G


Enzyme Substrate (ES) Enzyme Substrate (ES) ComplexComplex

Enzyme catalyzed reactions are independent of substrate concentration at high substrate concentrations

Catalyst has binding sites that can be saturated

● Once saturated, further increase of [substrate] will not increase rate of product formation

● ES ---> E + P (ie. k2) is rate determining and reaction

rate depends upon the [ES]

Note: E is enzyme, S is substrate, P is product and ES is the enzyme substrate complex

This rate equation is not directly useful as we require rate constants for each step AND the [ES] as a function of time

E + S ES E + Pk

1

k-1

k2

d[P ]

dt=k2[ES ]

d[ES ]

dt=k1[E ][S ]−k−1 [ES ]−k2[ES ]


Assumptions Assumptions

Using two assumptions, the reaction rate equation can be rewritten in terms that are experimentally measurable

(1) Steady State Assumption – [ES] stays constant during the measurement. Only valid when k

2 <<< k

1 or k

-1.

Typically valid for a short duration (initial velocity, vo) after the reaction starts and before

significant amounts of substrate (10%) have been converted to product (do not have to consider k

-2)

(2) Equilibrium Assumption – bind/release substrate is fast compared to catalysis (k

-1 >>> k

2) and reaches equilibrium.

[ES] depends upon k1/k

-1 (note: K

eq,association = k

1/k

-1 = [P]/[S])

E + S ES E + Pk

1

k-1

k2

E + S ES E + Pk

1

k-1

k2


Michaelis-Menten Equation Michaelis-Menten Equation

The rate of product formation is k2[ES]

From the steady state assumption d[ES]/dt = 0

- Allows us to solve for the [ES] term in our rate equation

- Substituting [E] = [ET] – [ES] (E

T is total Enzyme)

By definition, the maximum velocity of the enzyme catalyzed reaction occurs when [E

total] = [ES]

- Allows us to define Vmax

= k2 [E

T]

- Allows us to define KM = (k

-1 + k

2)/k

1

Result is the Michaelis-Menten equation; the basic equation of enzymology

Note: You are not responsible for deriving this equation. You do need to know the equation and those for V

max and K

M

v=d [P]

dt=k

2[ES ]=k

2

[ET][S ]

KM[S ]

vo=

Vmax

[S ]

KM[S ]

Vmax

=k2[E

T]

d[P ]

dt=k2[ES ]

d[ES ]

dt=k1[E ][S ]−k−1 [ES ]−k2[ES ]


KKMM – Michaelis constant – Michaelis constant

Plots of initial velocity vs. substrate concentration yield hyperbolic curves for Michaelis-Menten reactions

KM is the substrate concentration at which the reaction

velocity is ½ maximal

● assuming KM = [S], the Michaelis-Menten equation reduces

to vo=V

max/2

● small KM is associated with efficient catalysis at low [S]

When k2<<<k

-1, K

M is a measure of substrate

affinity

vo=V max [S ]

K M[S ]

KM=k−1k2

k1

=breakdownof ES

formationof ES≈ (k

-1/k

1) = (1/K

eq,assoc) = (K

eq,dissoc)


Analysis of Kinetic DataAnalysis of Kinetic Data

Several methods exist for determining the kinetic constants in the Michaelis-Menten equation

1) Initial velocity (vo vs [S]) plots require extrapolation of V

max

2) Lineweaver-Burke or double reciprocal plot

● Reciprocal of Michaelis-Menten equation (1/vo vs 1/[S])

slope = KM/V

max y intercept = 1/V

max x intercept = -1/K

M

● Better approach but nature of 1/[S] means most measurements are near the y axis. Small errors can skew calculation of constants

Other methods exist for treating kinetic data, each with its own strengths and weaknesses

vo=V max [S ]

K M[S ]

1vo

=K M[S ]

V max [S ]

1vo

=K M

V max

1[S ]

1

V max


kkcatcat (catalytic constant or turnover number)(catalytic constant or turnover number)

kcat

is the rate constant for the overall reaction at saturating substrate

● varies widely (108 times) among enzymes

Relationship between kcat

and rate constants (k1, k

-1, k

2, etc.) depends

upon the reaction mechanism

1) Michaelis-Menten mechanism (simplest case)

kcat

= k2

2) More complicated mechanisms

kcat

≤ k2 AND may depend on other rate constants

kcat=V max

[E ]T


kkcatcat / K / KM M (catalytic efficiency)(catalytic efficiency)

Catalytic efficiency depends upon both reaction rate and substrate concentration.

When [S] << KM,

very little ES is formed and the Michaelis-Menten equation reduces to

● second order rate equation with an apparent rate constant, (kcat

/KM)

The apparent rate constant (kcat

/KM) under these conditions is a measure of

catalytic efficiency

vo=

Vmax

[S ]

KM[S ]

vo=(V max [S ])

(K M)=(

(kcat)

(K M))[ET ][S ]


What is the upper limit to catalytic efficiency?

● efficiency is highest when k2 >> k

-1, and k

cat/K

M ≈ k

1

(Note: if k2 >>> k

-1, the enzyme does not have a Michaelis-Menten mechanism)

● rate constant (k1) for formation of ES limits catalytic efficiency

Theoretically, k1 can be no larger than the frequency with which enzyme and

substrate encounter one another

● diffusion rates define limits of enzyme efficiency and yield values in the 108-109 M-1s-1

range (Diffusion-controlled limit)

● several enzymes have kcat

/KM values in this range and must catalyze a reaction almost

every time they encounter a substrate

– Sometimes called 'catalytically perfect'

kkcatcat / K / KM M LimitsLimits

kcat

K M

=k2

K M

=k2 k1

k−1k2


Inhibitors are compounds that bind to enzyme in such a way that the activity of the enzyme is reduced

- many inhibitors resemble the enzyme's natural substrate but react slowly or not at all

● Commonly used to investigate the nature of the substrate-binding site and to elucidate enzyme mechanism

- many (most) clinical drugs are enzyme inhibitors produced synthetically or isolated from natural sources

● recently the first rationally 'designed' drugs have been utilized

Large portion of pharmacy is medicinal use of inhibitors

– must consider many issues over and above binding and inhibition

● dosage, solubility, side effects, cost, etc

InhibitionInhibition


Example of enzyme inhibitor used as chemotherapeutic agent

● dihydrofolate reductase catalyzes an essential step in the synthesis of dTMP

● methotrexate binds to and inhibits dihydrofolate reductase preventing dTMP biosynthesis

– preferentially kills actively dividing cells (eg cancer cells)

– clearly, methotrexate is structurally related to the normal substrate and is known to bind in the enzyme active site in a conformation similar but not identical to the substrate

Inhibitor - methotrexateInhibitor - methotrexate

(Red) Structural differences between natural substrate (dihydrofolate) and methotrexate

chapter 13: introduction to enzymes

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